Exact partitioning of affine dependence algorithms

Abstract

This paper presents a first approach to partition affine dependence algorithms (e.g., sets of affine recurrence equations, loop programs with affine data dependences) when mapped onto reduced/fixed size processor arrays with local interconnect. Existing approaches start with localized dependence algorithms (e.g., sets of uniform reccurence equations, uniform loop programs). These give up optimality with respect to 1) freedom of scheduling processor tiles, 2) memory requirements due to copy operations introduced by localization of data dependences prior to partitioning, and 3) they cause unnecessary control overhead due to intermediate statements. Our partitioning approach is able to partition affine dependence algorithms and therefore represents a substantial extension of previous partitioning approaches such as described in [10,14,15,11]. 4) We also propose the concept and methodology of partial localization that only localizes intra-tile or inter-tile data dependences, respectively, for the partitioned affine dependence algorithm.